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arXiv:2010.03014 · Physical Review Research

Photocount statistics of the Josephson parametric amplifier

Jean Olivier Simoneau, Stéphane Virally, Christian Lupien, Bertrand Reulet

Published Mar 4, 2022• 4 citations
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Abstract

Parametric amplifiers are known to squeeze the vacuum state of the electromagnetic field, thus the statistics of the photocounts at their output should be that of squeezed vacuum. However, several theoretical works predict a very different statistical distribution. We have measured the photocount statistics of a Josephson parametric amplifier and recover the expected squeezed vacuum statistics. We explain this discrepancy by showing theoretically how the photocount statistics is dictated by the detection process. Namely, most experiments will naturally measure a single mode of the electromagnetic field, while the aforementioned theoretical works implicitly describe massively multimode detection.

DOI
10.1103/physrevresearch.4.013176

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Parametric amplifiers are known to squeeze the vacuum state of the electromagnetic field, thus the statistics of the photocounts at their output should be that of squeezed vacuum. However, several theoretical works predict a very different statistical distribution. We have measured the photocount statistics of a Josephson parametric amplifier and recover the expected squeezed vacuum statistics. We explain this discrepancy by showing theoretically how the photocount statistics is dictated by the detection process. Namely, most experiments will naturally measure a single mode of the electromagnetic field, while the aforementioned theoretical works implicitly describe massively multimode detection.
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We are engaged in an experimental effort to generate and detect squeezed vacuum fluctuations at microwave frequencies using a Josephson parametric amplifier. We have demonstrated 42% deamplification of 4.2-K thermal noise at 19.4 GHz. At this frequency the vacuum fluctuation noise is an order of magnitude smaller than 4.2-K thermal noise. We have installed cryogenic HEMT amplifiers in our apparatus, thereby increasing the detector sensitivity by an order of magnitude. Josephson parametric amplifiers have been notorious for exhibiting excess noise whose origin is still controversial. We have performed a systematic study of the noise performance of our device both below and above threshold in a variety of modes of operation. The experiments indicate that the excess noise in our device arises from low-frequency noise (0-20 MHz) propagating down dc bias lines. When an intense coherent oscillation is present in the signal passband, such as the pump when the amplifier is in the four-photon mode or the period doubled oscillations when the amplifier is operated in the three-photon mode above threshold, the low- frequency noise mixes with the coherent oscillation to generate noise sidebands in the amplifier's passband. Nevertheless, in suitable conditions, extremely low noise and high gains were achieved.
We derive a closed-form expression for the number probability distribution of a ``generic'' two-mode field in a two-mode squeezed state. We discuss its dependence on the average particle number in the two modes and on the amount of squeezing. We show that the distribution exhibits oscillations for particle numbers appropriately greater than the average, similar to the one-mode case, although the conditions under which such an oscillatory behavior occurs are different. These results are directed to the investigation of nonclassical properties in the radiation field produced by a parametric amplifier operated in a two-mode regime.
Experiments on generating squeezed microwave radiation at 19.16 GHz using a Josephson parametric amplifier were performed. The source of the radiation was cooled by a dilution refrigerator down to the lowest temperature of 0.030 K. At this temperature, noise at the input port of the parametric amplifier consists almost entirely of the vacuum fluctuations with a noise temperature h nu /2k of 0.46 K. The authors observed the squeezing of the microwave noise by 47+or-8% as referred to the input of the Josephson parametric amplifier. The measured double-sideband noise temperature of the amplifier is 0.446 K, which is comparable to the vacuum noise level.
Two-mode squeezed vacuum states are a crucial component of quantum technologies. In the microwave domain, they can be produced by the Josephson ring modulator that acts as a three-wave mixing nondegenerate parametric amplifier. Here, we numerically solve the full master equation of three bosonic modes describing the Josephson ring modulator to compute squeezing of output fields and gain at low signal power. We show that the third-order interaction from the three-wave mixing process intrinsically limits squeezing and reduces gain. Since our results are related to other general cavity-based three-wave mixing processes, these imply that any nondegenerate parametric amplifier will have an intrinsic squeezing limit in the output fields.
Josephson parametric amplifiers (JPA) are promising devices for applications in circuit quantum electrodynamics and for studies on propagating quantum microwaves because of their good noise performance. In this work, we present a systematic characterization of a flux-driven JPA at millikelvin temperatures. In particular, we study in detail its squeezing properties by two different detection techniques. With the homodyne setup, we observe the squeezing of vacuum fluctuations by superposing signal and idler bands. For a quantitative analysis, we apply dual-path cross-correlation techniques to reconstruct the Wigner functions of various squeezed vacuum and thermal states. At 10 dB signal gain, we find 4.9 ± 0.2 dB squeezing below the vacuum. In addition, we discuss the physics behind squeezed coherent microwave fields. Finally, we analyze the JPA noise temperature in the degenerate mode and find a value smaller than the standard quantum limit for phase-insensitive amplifiers.